Suppose that you discount the future hyperbolically. Assume that both b and d are strictly greater than zero but strictly smaller than one. At t 5 0, you are given the choice between the following three options: a (1 utile at t 5 0), b (2 utiles at t 5 1), and c (3 utiles at t 5 2). As a matter of fact, at t 5 0 you are indifferent between a and b and between b and c.

(a) Compute b and d.

(b) Suppose, in addition, that at t 5 0 you are indifferent between c and d (x utiles at t 5 3). What is x?